<h2>Problem 42</h2>
<div style="color:#666;font-size:80%;">25 April 2003</div><br />
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<p>The <i>n</i><img src="" style="display:none;" alt="^(" /><sup>th</sup><img src="" style="display:none;" alt=")" /> term of the sequence of triangle numbers is given by, <i>t<img src="" style="display:none;" alt="_(" /><sub>n</sub><img src="" style="display:none;" alt=")" /></i> = &frac12;<i>n</i>(<i>n</i>+1); so the first ten triangle numbers are:</p>
<p style='text-align:center;'>1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...</p>
<p>By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = <i>t</i><img src="" style="display:none;" alt="_(" /><sub>10</sub><img src="" style="display:none;" alt=")" />. If the word value is a triangle number then we shall call the word a triangle word.</p>
<p>Using <a href='project/words.txt'>words.txt</a> (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words?</p>
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